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Analytical Expressions for Isotropic Mixing in Three- and Four-Spin Topologies in 13C Systems
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| Journal of Magnetic Resonance, Series A |
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An important aspect of HCCH-TOCSY-based multidimensional experiments of 13C-labeled proteins and nucleic acids is the optimization of 13C-13C TOCSY mixing time. For this purpose, one needs a description of the mixing-time dependence of the magnetization transfer between various spins. Here, analytical expressions have been obtained for three- and four-spin systems found in amino acids, assuming isotropic-mixing conditions and a uniform one-bond 13C-13C coupling constant. These results, which require analytical determination of eigenvalues and eigenvectors of the isotropic-mixing Hamiltonian, were obtained using the program Mathematica for performing the essential linear algebra. The expressions are in complete agreement with numerical calculations carried out by Eaton et al. From these expressions, optimum magnetization transfer efficiencies for various spin topologies are easily obtained as a function of J and the mixing time t. The isotropic-mixing results agree reasonably well wth simulations employing mixing sequences such as IICT-1.
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